Goals from Luyolo Nomandela and Sadat Ouro-Akoriko handed Ea Lla Koto the win, while the Urban Warriors responded through Grandwald Scott.
Besides from their goal, Ajax were virtual spectators and had it not have been for the acrobatics of Sander Westerveld between the sticks, the scoreline could have read a lot worse.
Nonetheless, the visitors did have the best chance in the opening stages of the game when Toriq Losper fired straight at the keeper from close range in the 16th minute.
Nomandela, however, made no such mistake four minutes later with a clinical finish from inside the box to give Stars the lead.
Ajax, however, were not to be outdone and quickly hit back; Scott finding the equaliser in the 28th minute after Kennedy Mweene failed to deal with an initial Nhlanhla Shabalala shot.
Thereafter it was all Stars and it seemed only a matter of time before they regained the lead, which they did seconds before the half-time whistle through Ouro-Akoriko.
The second 45 did not see Ajax mount a comeback as they struggled to create any decent chances in front of goal.
Instead, it was the home side who looked more threatening, with Westerveld denying Nomandela in the 71st minute and then Paulus Masehe in the 77th minute with two fantastic saves.
The result moves Stars up to eighth, and leaves Ajax languishing down in 13th place.